The equilibrium of particles electrostatically confined by external forces and the competition between the electrostatic interaction and gravitational field

This study sets out to describe the interaction of charged confined particles with a gravitational field. The system consisted of charged particles interacting electrostatically between themselves and with a confining box whose walls have a linear charge distribution. We studied numerically several configurations including the introduction of a tilt, that takes into account the Earth’s gravitational field. In our analysis, we included the $\alpha$ parameter for describing the position of the center of mass and its evolution according to the influence of the box size. We also studied in detail the competition between the gravitational field and electrostatic forces over the system. Such a competition determines the shape and size of the distributed charges. When the electrostatic force is dominant, the charges are distributed almost symmetrically. Whereas, when the gravitational field is preponderant, the distribution of particles tends to have a hive-like shape and then as the tilt angle increases the distribution is flattened. This effect is exacerbated when the particles have bigger masses and the inclination is higher. From a physical analysis, we obtained an expression to determine the center of mass of the distributed particles, depending on the box’s size and other physical parameters. Finally, based on the data analysis, we obtained fitting equations for the gravitational (logarithmic) and electrostatic (exponential) energies as a function of the enveloping area.